Show that `int_0^(pi/2)sqrt((sin2theta))sinthetadtheta=pi/4`

Evaluate: int_(0)^(pi//2) sqrtsinthetacos^(5)theta d theta

Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n in Z) (a) npi-pi/4 (b) npi+pi/(12) (c) npi+pi/6 (d) none of these

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

If int_0^(pi/2)logsinthetad(theta)=k , then find the value of int_0^(pi/2)(theta/(sintheta))^2d(theta) in terms of k

If int_0^(pi/2)logsinthetadtheta=k , then find the value of int_pi^(pi/2)(theta/(s intheta))^2dtheta in terms of k

Evaluate the following : int_(0)^((pi)/(2)) sin^(3) theta cos^(5) theta d theta

The expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) is positive for all theta in (a) (2npi-(3pi)/4,2npi+pi/4),n in Z (b) (2npi-pi/4,2npi+pi/6),n in Z (c) (2npi-pi/3,2npi+pi/3),n in Z (d) (2npi-pi/4,2npi+(3pi)/4),n in Z

If 0 leq theta leq pi and sin(theta/2)=sqrt(1+sintheta)-sqrt(1-sintheta) ,then the possible value of tan theta , is -

If pi/2 lt theta lt 3 pi/2 then sqrt( (1-sin theta)/(1+ sin theta )) - tan theta is